setmemb_nlms.m

System identification with adaptive filter using full and partial-update Normalised-Least-Mean-Squar

function [e,u,w] = setmemb_nlms(x,d,N,M,w0,epsilon,gamma)
%[e,w] = setmemb_nlms(x,d,N,M,w0,mu,epsilon,gamma) implements the set
%membership selective partial update NLMS algorithm. 
%   ----------------
%   input parameters
%   ----------------
%   x : Lx1 input signal
%   d : Lx1 desired response 
%   N : filter length
%   M : number of coefficients to be updated
%   w0 : Nx1 initialization
%   epsilon: regularization parameter (to avoid divide by zero)
%   gamma: bound on a posteriori error
%   ----------------
%   function outputs
%   ----------------
%   w : LxN evolution of coefficients
%   u : vector of 1s and 0s, if an update occurs at iteration k, kth
%           entry is 1, else 0.
%   e : Lx1 error vector

x = x(:);
d = d(:);
w0 = w0(:);

L = length(x);
w = zeros(L,N);
e = zeros(L,1);
u = zeros(L,1);

w(1,:) = w0';
xvec = zeros(N,1);

for i = 1:L-1
    xvec = [x(i);xvec(1:N-1)];
    e(i) = d(i)-w(i,:)*xvec;

    [xs,ix] = sort(-abs(xvec));     %rank
    de = zeros(1,N);
    de(ix(1:M)) = 1;
    IM = diag(de);
    
    if abs(e(i)) > gamma,
        mu = (1-gamma/abs(e(i)))*(1+epsilon/norm(IM*xvec)^2);
        upd = mu*e(i)*IM*xvec/(norm(IM*xvec)^2+epsilon);
        u(i) = 1;
    else
        upd = zeros(N,1);
    end
    
    w(i+1,:) = w(i,:) + upd';
end
xvec = [x(L);xvec(1:N-1)];
e(L) = d(L)-w(L,:)*xvec;